Josephson Effect in a Coulomb-blockaded SINIS Junction

TL;DR

This paper analyzes the Josephson current in Coulomb-blockaded SINIS junctions, deriving a comprehensive free energy expression that captures the transition from weak to strong Coulomb interactions and reveals non-sinusoidal current-phase relations.

Contribution

It provides a full expression for the free energy of Coulomb-blockaded SINIS junctions valid at any Coulomb strength, unifying weak and strong interaction regimes.

Findings

Current-phase relation is non-sinusoidal across Coulomb strengths.

A local minimum in current appears at intermediate phase differences.

The derived formula interpolates between known weak and strong Coulomb interaction results.

Abstract

The problem of Josephson current through Coulomb-blocked nanoscale superconductor-normal-superconductor structure with tunnel contacts is reconsidered. Two different contributions to the phase-biased supercurrent are identified, which are dominant in the limits of weak and strong Coulomb interaction. Full expression for the free energy valid at arbitrary Coulomb strength is found. The current derived from this free energy interpolates between known results for weak and strong Coulomb interaction as phase bias changes from 0 to pi. In the broad range of Coulomb strength the current-phase relation is substantially non-sinusoidal and qualitatively different from the case of semi-ballistic SNS junctions. Coulomb interaction leads to appearance of a local minimum in the current at some intermediate value of phase difference applied to the junction.